The two top diplomats are in daily contact on the matter and sealed a deal in Geneva last weekend aimed at dismantling the Damascus regime's arsenal of these types of banned arms.
While welcoming his Dutch counterpart Frans Timmermans to the State Department, Kerry told reporters he had had a fairly long phone conversation with Lavrov earlier in the day.
"We talked about the cooperation which we both agreed to continue to provide, moving not only towards the adoption of the OPCW (Organisation for the Prohibition of Chemical Weapons) rules and regulations, but also a resolution that is firm and strong within the United Nations," Kerry said.
Timmermans, meanwhile, said the Netherlands and the United States were "exactly on the same page."
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"In the UN, we see eye to eye as to the content of the United Nations Security Council resolution, which should be very firm on making sure that Assad, who doesn't have a track record of actually doing what he promises, does what he has promised now," he said, referring to Syrian President Bashar al-Assad.
Yesterday, Kerry said the UN Security Council must be prepared to agree to a binding resolution on Syria's chemical weapons next week.
Russia, a key ally of Damascus, opposes all references to a possible use of force.
Just as Kerry and Timmermans were speaking, the Organisation for the Prohibition of Chemical Weapons said it had received initial details on Syria's program and arsenal, which it has been tasked with dismantling.